Sugru wouldn't set hard enough, and you'd have to leave it in place overnight anyway. I'd go for Polymorph (called Shapelock in the US), which sets rigid in a couple of minutes.

How mushy is Sugru? Maybe a syringe and a tube, along with a hollow needle to defeat air bubbles. That plastic goop for fixing headlights that hardens under ultraviolet seems a likely candidate. You'd just want to make sure none of that seeped in past the screw.